Halim Zeghdoudi , Lazri Nouara , Djabrane Yahia
ARTICLE

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ABSTRACT

In this paper, we introduce a new Lindley Pareto distribution, which offers a more flexible model for modelling lifetime data. Some of its mathematical properties like density function, cumulative distribution, mode, mean, variance, and Shannon entropy are established. A simulation study is carried out to examine the bias and mean square error of the maximum likelihood estimators of the unknown parameters. Three real data sets are fitted to illustrate the importance and the flexibility of the proposed distribution.

KEYWORDS

T-X family, Lindley distribution, Pareto distribution.

REFERENCES

ABOUELMAGD, T. H. M, AL-MUALIM, S., AFIFY, A.Z. AHMAD, M., ALMOFLEH, H., (2018). The odd Lindley Burr XII distribution with applications. Pak. J. Statist. 34(1), pp. 15–32.

AKINSETE, A., FAMOYE, F., LEE, C., (2008). The beta-Pareto distribution, Statistics, 42, pp. 547–563.

ALZAATREH, A., LEE, C., FAMOYE, F., (2013a). A new method for generating families of continuous distributions. Metron. 71(1), pp. 63–79.

ARLOND, B. C., BALAKRISHNAN, N., (1989). Relations, bounds and approximations for order statistics. Lecture Notes in Statistics Vol. 53, Springer-Verlag, New York.

ASGHARZADEH, A., BAKOUCH, H. S., ESMAEILI, L., (2013). Pareto Poisson–Lindley distribution with applications. J. of Applied Statistics, 40(8), pp. 1717–1734.

COORAY, K., (2006). Generalization of the Weibull Distribution: The Odd Weibull Family. Statistical Modelling, 6, pp. 265–277.

GHITANY, M. E., AL-MUTAIRI, D. K., NADARAJAH S., (2008a). Zero-truncated Poisson-Lindley distribution and its application, Math. Comput. Simulation, 79, pp. 279–287.

GHITANY, M. E., ATIEH, B. NADARAJAH, S., (2008b). Lindley distribution and its applications. Math. Comput. Simulation, 78, pp. 493–506.

GOMES-SILVA, F.S., PERCONTINI, A., DE BRITO, E., RAMOS, M. W., VENÂNCIO, R., CORDEIRO, G. M., (2017). The odd Lindley-G family of distributions. Austrian Journal of Statistics, 46(1), pp. 65–87.

LEE, E.T., WANG, J.W., (2003). Statistical Methods for Survival Data Analysis, 3rd edn. Wiley, Hoboken.

LEHMANN, E.L., SCHEFFÉ, H., (1950). Completeness, similar regions, and unbiased estimation. Sankhya, 10, pp. 305–340. —

LINDLEY, D. V., (1958). Fiducial distributions and Bayes’ theorem. Journal of the Royal Society, series B,20, pp. 102–107.

MÄKELÄINEN, T., SCHMIDT, K., STYAN, G.P.H., (1981). On the existence and uniqueness of the maximum likelihood estimate of a vectorvalued parameter in fixed-size samples, The Annals of Statistics, 9(4), pp. 758–767.

MAHMOUDI, E., (2011). The beta generalized Pareto distribution with application to lifetime data. Mathematics and Computers in Simulation, 81, pp. 2414–2430.

PARETO, V., (1896). Essai sur la courbe de la répartition de la richesses. Faculté de droit a l’occasion de l’exposition nationale suisse, Geneve, Université de Lausanne.

PICKANDS, J., (1975) Statistical inference using extreme order statistics. Annals of Statistics, 3, pp. 119–131.

RÉNYI, A., (1961). On measures of entropy and information. In: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, I, University of California Press, Berkeley, pp. 547–561.

SHANNON, C. E., (1948). A mathematical theory of communication. Bell System Technical Journal, 27, pp. 379–432.

SANKARAN, M., (1970). The discrete Poisson-Lindley distribution. Biometrics, 26, pp. 145–149.

SHARMA, M., SHANKER, R., (2013). A two-parameter Lindley distribution for modeling waiting and survival times data, Applied Mathematics, 4, 363-368.

ZAKERZADAH, H. , DOLATI, A., (2010). Generalized Lindley distribution. J. Math. Ext, 3(2), pp. 13–25.

ZEA, L.M., SILVA, R.B., BOURGUIGNON, M., SANTOS, A.M., CORDEIRO, G.M.,(2012). The beta exponentiated Pareto distribution with application to bladder cancer susceptibility. International Journal of Statistics and Probability, 1, pp. 8–19.

ZEGHDOUDI, H., NEDJAR, S., (2016). Gamma Lindley distribution and its application. Journal of Applied Probability and Statistics. 11(1), pp. 129–138.

ZEGHDOUDI, H., NEDJAR, S., (2016). On gamma Lindley distribution: Properties and Simulations. Journal of Computational and Applied Mathematics, 298, pp. 67–174.

ZEGHDOUDI, H., LAZRI, N., (2016). On Lindley-Pareto Distribution: Properties and Application. Journal of Mathematics, Statistics and Opera tions Research (JMSOR), Vol. 3, No. 2

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